cp's OEIS Frontend

A320024 The odd part of those numbers which divide the sum of their divisors (A007691).

%I A320024 #22 Oct 31 2020 01:39:59
%S A320024 1,3,7,15,31,21,127,945,4095,1023,544635,46035,8191,355725,279279,
%T A320024 1796165,5388495,180213,131071,110800305,249987465,42833475,3112865,
%U A320024 8109585,524287,9338595,49198149,253255275,22017975903,13341660255,30101431815,709933138551
%N A320024 The odd part of those numbers which divide the sum of their divisors (A007691).
%C A320024 The data was derived from the data in A007691.
%C A320024 The Mersenne primes A000668 are a subsequence; in fact a prime is in this sequence if and only if it is a Mersenne prime.
%C A320024 Note that John Voight's 'spoof odd perfect number' 22017975903 is included. - _Peter Luschny_, Oct 30 2020
%H A320024 Alois P. Heinz, <a href="/A320024/b320024.txt">Table of n, a(n) for n = 1..1600</a>
%H A320024 BYU Computational Number Theory Group, <a href="https://arxiv.org/abs/2006.10697">Odd, spoof perfect factorizations</a>, arXiv:2006.10697 [math.NT], 2020.
%H A320024 J. Voight, <a href="https://math.dartmouth.edu/~jvoight/articles/opn-mass-rev-060211.pdf">On the nonexistence of odd perfect numbers</a>.
%F A320024 a(n) = A000265(A007691(n)).
%p A320024 a_list := proc(len) local L, n; L := NULL; for n from 1 to len do
%p A320024 if numtheory:-sigma(n) mod n = 0 then L := L, n/2^padic[ordp](n, 2) fi od; L end:
%t A320024 A007691 = Select[Range[1000000], Divisible[DivisorSigma[1, #], #] &]; Table[A007691[[n]]/2^IntegerExponent[A007691[[n]], 2], {n, 1, Length[A007691]}] (* _Vaclav Kotesovec_, Oct 14 2018 *)
%Y A320024 Cf. A000265, A000668, A007691.
%K A320024 nonn
%O A320024 1,2
%A A320024 _Peter Luschny_, Oct 03 2018